In Harry Potter and the Philosopher's Stone, it is said that Dumbledore has a
very odd watch. It had twelve hands but no numbers; instead, little planets were moving around the edge.
Philosopher's Stone, The Boy Who Lived (Ch. 1)
In DH, Harry is given Fabian Prewett's watch, which is quite the same except that it is dented on the back. Yet, "usual" watches work since Harry has one in GoF (even if it doesn't work anymore) :
Harry took off his watch, which he was only wearing out of habit, as it didn't work anymore [...]
Goblet of Fire, prior to the Niffler's lesson
So, why do wizards use those watches ? Is there any explanations on how does it work ? Is it more precise than our watches ?